Two-point Padé approximants to Stieltjes series representation of bulk moduli of regular composites

  • Stanisław Tokarzewski Institute of Fundamental Technological Research Polish Academy of Sciences
  • Józef Joachim Telega Institute of Fundamental Technological Research Polish Academy of Sciences

Abstract

The aim of this contribution is to present two-point Padé approximants method for the determination of upper and lower estimates on the effective transport coefficients of two-phase composite materials. The obtained formulae improve the corresponding one-point Padé approximants bounds [1,2,4,14,23] . As an example, a set of narrowing bounds for the overall conductivity of a square array of cylinders has been evaluated.

Keywords

References

[1] G.A. Baker. Essentials of Padé Approximants. Acad. Press, London, 1975.
[2] G.A. Baker, P. Graves-Morris. Padé Approximants. Part I: Basic Theory. Encyclopedia of Mathematics and its Applications, 13, Addison- Wesley Publ. Co., London, 1981.
[3] G.A. Baker, P. Graves-Morris. Pade Approximants, Part II: Extensions and Applications. Encyclopedia of Mathematics and its Applications, 14, Addison-Wesley Publ. Co., London, 1981.
[4] D.J . Bergman. The dielectric constant of a composite material - A problem in classical physics, Phys. Report., C 43: 377- 407, 1978.
[5] A. Bultheel. Laurent Series and their Padé Approximants. Birkhäuser-Verlag, Basel, 1987.
Published
Jul 14, 2023
How to Cite
TOKARZEWSKI, Stanisław; TELEGA, Józef Joachim. Two-point Padé approximants to Stieltjes series representation of bulk moduli of regular composites. Computer Assisted Methods in Engineering and Science, [S.l.], v. 3, n. 2, p. 121-132, july 2023. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/1450>. Date accessed: 22 dec. 2024.
Citation Formats
Issue
Vol 3 No 2 (1996)
Section
Articles
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